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Robert Mullins, Legal Positivism and Deontic Detachment, 31 Ratio Juris 4 (2018).

It is curious that Anglophone philosophers of law (many of whom have had some training in logic in conjunction with the classwork required for a Ph.D.) ignore deontic logic — the branch of logic that deals with propositions that employ normative concepts like obligation and permission. The point is not that deontic logic can answer problems in the philosophy of law, but that it can help reveal them. This very short paper by Robert Mullins is a wonderful example. It concerns the apparent incompatibility between a commonly accepted inference rule in deontic logic, deontic detachment, and the core principle of positivism, the social thesis.

According to deontic detachment, the following reasoning is valid (if the premises are true, the conclusion must be true):

1) It ought to be that if P then Q.
2) It ought to be that P.


3) It ought to be that Q.

Mullins’s legal example is a law obligating all those who file income taxes to do so by the close of business Friday and another law obligating one to file income taxes. It follows from deontic detachment that one is obligated to file income taxes by the close of business Friday.

Now for the social thesis. Mullins’s formulation is controversial:

Legally it ought to be that φ if and only if the proposition that it ought to be that φ is accepted by legal officials.

Given this understanding of the thesis, there is indeed a conflict with deontic detachment. Although the premises in Mullins’s legal example are accepted by legal officials, the conclusion (that one ought to file income taxes by the close of business Friday) need not be. But that doesn’t matter to its status as a legal fact.

Now someone might question whether legal officials might not accept the conclusion. True, there is no law under which one ought to file income taxes by the close of business Friday. But officials, putting two and two together, would surely have accepted that fact. But as the number of laws (and other law-making acts) increases, one will reach a point at which there are many legal consequences that have not been entertained by any official, much less the bulk of officials. That does not appear to make a difference to their status as legal facts.

What is more, Mullins argues that other rules besides deontic detachment can generate legal facts that outstrip official acceptance. Assume that there is a law under which one ought not camp on public property. Employing closure under logical consequence, it is also the case that Fred ought not camp on public property, and that he ought not do so on Wednesday, and that he not do so on Wednesday while wearing a brown suit. But none of these legal facts has been entertained by legal officials.

Mullins emphasizes those unacknowledged legal facts that follow from laws. But at times laws themselves can be unrecognized. It is possible for a law to have been enacted without the lawmaker, or other officials, being aware of that fact. Accidental lawmaking can occur.

Mullins’s initial account of the social thesis is too strong, however. The usual way that the thesis is put is that the existence and content of the law (or, alternatively, all legal facts) ultimately depend solely upon social facts. The core social facts upon which legal facts ultimately depend do indeed concern acceptance by a community’s officials, but positivists do not insist on a one-to-one correspondence between the legal fact that φ and officials’ accepting that φ. What is required is official acceptance of fundamental rules of the legal system. The legal fact that the United States Constitution is binding ultimately depends upon American officials’ accepting that it is. But countless other legal facts concerning the American legal system can obtain without American officials’ recognizing them at all.

In the end, this is precisely the point that Mullins seeks to make. The social thesis must construe official acceptance narrowly, in a way that allows legal facts to outstrip official attitudes. And this is, I believe, an exceptionally important point — the implications of which have not always been taken to heart by positivist philosophers of law. If the legal fact that φ can obtain even though officials do not accept that φ, there must be some facts other than social facts about official acceptance by virtue of which it is a legal fact that φ. What are those other facts?

I think positivist philosophers of law should concede that the requisite facts concern abstract objects: facts about the fundamental rules of the legal system and facts about the rules that are identified as laws by those fundamental rules. Although this point has not been widely recognized by positivists, I think some would be quite willing to concede this role played by abstract-object facts in determining legal facts. See Shapiro, Legality 102-04 (2011).

An analogy with a language is appropriate here. Some philosophers of language understand languages as abstract objects — in particular, functions from strings of scribbles or phonemes to propositions (which are themselves abstract objects). Under the abstract object that is French, “Il pleut” takes one to the proposition it-is-raining. Such facts about French are not social. They can’t be, for there is an infinite number of such facts about French, more than any person could ever entertain. Nevertheless, what makes it such that the French speak French — what connects them to that abstract object (rather than, say, to Esperanto) — is social facts about the French people.
Positivists should take the same approach. The abstract object that is the American legal system is not social. It can’t be, for (as Mullins shows) there are more facts about this system than can ever be entertained by American officials. But what makes it such that Americans have the American legal system — what connects them to that abstract object — is social facts about American legal practices, in particular, facts about official acceptance.

This is a relatively limited challenge to positivist theories of law. A prominent theme in Ronald Dworkin’s writings is the existence of theoretical disagreements, in which officials disagree about even the fundamental rules of the legal system, while nevertheless thinking that their disagreement has a preexisting legal answer. Dworkin, in effect, argues that social facts about official acceptance cannot determine what legal system should be assigned to a community. That can be done only if we include moral facts as well. This challenge to positivism takes us well beyond the one presented in Mullins’s paper.

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Cite as: Michael Green, Deontic Logic and the Philosophy of Law, JOTWELL (July 7, 2020) (reviewing Robert Mullins, Legal Positivism and Deontic Detachment, 31 Ratio Juris 4 (2018)),